Go the heat gun route. Try a hair dryer if you have to, it may not work...but you can try.
If that does not do it, rent, or purchase a heat gun.Work for the closest edge, get the putty knife ready, and a couple of chopsticks or wood skewers for cooking, put them in there to keep it separated so it does not stick back right away.
Then glue it back together. You may need some clamps to hold it firm, with some boards to span the entire section of the cabinet...makes the clamp area bigger...once you start you will get the idea.
Good luck, and open a window.