I water down wood glue a little so it will flow from a syringe like for injecting medications. Use the needle and inject some glue in the cracks place some wax paper over the area. I would remove the head and lay the cabinet on its back. Now you can place a flat piece of wood over the wax paper and place something heavy to clamp the veneer in place a brick or a bucket with some rocks in it. If you have clamps large enough you can use them. Let glue cure over night.