There are usually different MCTs for Domestic-Domestic and Domestic-International. I don't doubt that 35 minutes is the D-D connection time but it seems unlikely that it would also be the D-I MCT.

I'd DEFINITELY try calling in and see if you can get booked on an earlier flight to LAX - 35 minutes is fine if everything goes well, but one hiccup (landing at T6 into LAX, any delay on the outbound) and you will be in trouble.

EDIT: 35 minutes is in fact the D-I connection time (weird). I still think you should try calling.