Not sure how useful this following information is, but I just thought it should belong here.
Each influence level increase Every two levels (at least past level 10 influence) with those four Odessan people....Hylo, the Hutt, Sena-Rae, etc...Y'know, those people...Rewards you with 20 Common Crystals, 10 Glowing, and 5 Radiant.
EDIT with further info.
It is in fact every two levels of influence, at any level/rank, that the reward is 20 Common, 10 Glowing, and 5 Radiant.
That is very, very significant, especially if you have a bunch of those crates stored away somewhere.