[OldRestorer]

There are a few wood blocks in the bottom inside the cabinet right?
They have screws behind them.
At least they were in mikes 90 cabinet. Yes there is some glue so watch out for veneer peeling. 

You can see in my pic that it peeled some of the inside wood but not the face.
You can also see the 2 holes that held screws behind the wood blocks.

Use a plastic credit card from the outside it if you have a razor scraper for carpentry that will be thinner and stronger...