Hi frigidxarch,
the short answer is that it really depends on how schools might classify your profile (e.g., URM vs ORM).
A 665 GMAT FE score roughly maps to a 710-720 on the Classic test, which is below average for your reach and target schools.
Given your relatively short work experience at matriculation, I'd say even a small bump to 675 could significantly increase your odds, but I'd try to score at least 685.
Of course, as you may have heard multiple times, your GMAT score is just one piece of the puzzle and, alone, won't either grant you admission nor lead to a rejection straightaway. So, even with your current score and a kick-ass application, admission is still possible.
I hope that helps.
Warm regards,
Alex