The major differences between the Septuagint and the Masoretic text is in the year of Methuselah's death and in the presence of Cainan as the son of Arphaxad and father of Salah in the Septuagint, but not in the Masoretic (or Samaritan) text.
There is no earlier manuscript available to us that explains the discrepancy in the year of Methuselah's death, but it is possible to consider reasons for the change. If he died in the year of the Flood and was killed by God along with all the evil inhabitants of the earth, either he was himself evil and deserved to die, or Noah was unwilling to help his righteous grandfather. If he died years after the Flood in spite of not having been on the Ark, then the story of the Ark is in some way flawed. If the first problem exercised the minds of the Septuagint compilers, this could have been solved by having Methuselah live beyond the Flood. If, instead, the earliest versions of the genealogy was discovered to have Methuselah live through the Flood when all except Noah and his family should have died, then the scribes in the lines of the Masoretic and Samaritan texts could have made some small adjustments to the genealogy to ensure this did not happen, thereby preserving the Flood story.
There is also no earlier manuscript available to us that explains the discrepancy in respect to Cainan, but there is a later reference. Luke's Gospel has Cainan in the ancestry of Jesus (Luke 3:36). If Luke's genealogy is literally true, then this is confirmation of the Septuagint against the Masoretic and Samaritan texts. Otherwise, it would simply be consistent with Luke's use of the Septuagint for Old Testament references.
However, Eric Lyons (Apologetics Press) points out that the oldest Septuagint manuscripts do not include Cainan in its genealogy, and he is not mentioned by early writers who are known to have used the Septuagint. Lyons goes on to provide support for the Septuagint having been altered to conform with the genealogy we now find in Luke's Gospel:
Many are quick to point out that the Septuagint (the Greek translation of the Hebrew Old Testament) mentions the name Cainan, and thus verifies that he was the son of Arphaxad, just as Luke 3:36 indicates. The problem with this line of defense is that the oldest Septuagint manuscripts do not include this reference to Cainan (Sarfati, 1998, p. 40). Patrick Fairbairn indicated in his Bible encyclopedia that this Cainan does “not appear to have been in the copies of the Septuagint used by Theophilus of Antioch in the second century, by Africanus in the third, or by Eusebius in the fourth” (1957, p. 351). He goes on to state that it also was left out of the Vatican copy of the Septuagint (p. 351). That “Cainan” was a later addition to the Septuagint (and not a part of it originally) also is evident from the fact that neither Josephus nor Africanus mentioned him, and yet all indications are that they both used the Septuagint in their writings. [They repeat too many of the same numbers of the Septuagint not to have used it.] Thus, as Larry Pierce concluded, “It appears that at the time of Josephus, the extra generation of Cainan was not in the LXX [Septuagint—EL] text or the document that Josephus used, otherwise Josephus would have included it!” (1999, p. 76). As Henry Morris concluded in his commentary on Genesis: “[I] t is altogether possible that later copiers of the Septuagint (who were not as meticulous as those who copied the Hebrew text) inserted Cainan into their manuscripts on the basis of certain copies of Luke’s Gospel to which they then had access” (Morris, 1976, p. 282).
The author of Luke had good reason to insert an additional ancestor in his genealogy at this point, just as he adds another ancestor, Admin, as the son of Aram and father of Amminadab (Luke 3:33, omitted in some English translations). By this means, he was able to have great men occur at intervals of 7 generations (including Abraham at 21 and David at 35), with Jesus born on the 77th generation after Adam. While this is not proof, it provides credible reasons for Luke's genealogy being the source for including Cainan in the Septuagint if the earliest versions of the Septuagint did not include his name.