Given where the cracks are, I would try to spread them a bit, and get some Gorilla Glue in there.
If you use Gorilla Glue, it will expand, and require you to touch up the outside of the cabinet, but will be stronger than the original wood.
You are going to need a couple bar clamps, or a band clamp with a call block across the front.
Once the glue is set on the original cracks, I would reinforce it by gluing small chunks of wood across the inside.
The glued panels on the inside should prevent any separations from occurring just outside the glue joint.