Depending on how wide the split is, you could try forcing some Titebond II or III wood glue in the crack with an acid brush and clamp it together. While the glue is still wet, after clamping, wipe the excess off with a damp cloth or paper towel. Leave it clamped for a few hours, but don't try to squeeze the life out of it with the clamps.
I managed to bust a cabinet door with a slide once and repaired it good as new. Luckily, the mirror insert didn't break, just the joints between the rails and one stile.