It is hard to tell from your image what type of wood you are dealing with.
Remove the speaker and check that the frame was not bent. Lie it face down on a flat surface and look for warping. Test the speaker.
If the the cabinet is plywood, apply a good carpenters glue like Titebond II or III into the crack and clamp. If any chunks have come out you can fill them with an
epoxy putty like this product. Similar products are available at hardware store plumbing departments. As far as I know, the difference is that the wood store products have a longer setup time. It makes it a bit easier to work with.
If the wood is particle board, it is harder to fix well. I have had good results by breaking off badly cracked or crumbled areas and building them up again with the epoxy. Then sand and reshape the area. You can drill the epoxy and it holds T-nuts but it is best to install them before the epoxy cures. Finally, repaint the area.
