I recently had this done to my 1971 D18 by an authorized Martin repair station and a luthier whom I know and trust.

I have also had this done to a gibson J45.

What is generally the cause is that the top is bellying upward. The bridge will have to be removed and the top braced and clamped to "flatten" out the top again. Once this is done, the bridge can be glued and clamped. My guy wants these to sit in the clamps for both the top and the bridge a week or so each. He feels that his way will secure and hold for 50 years.

With the respect that I have for Martin instruments, I strongly suggest that you have this done by a qualified and experienced guitar repairperson. Expect to pay $200-250. For a quality instrument such as your D35, this is not something that you want to skimp on or shop around looking to save a few bucks.

Go with the best most qualified person that you can find.