yeah I do that off and on, shits me up the wall.

I cut a small oversized square of teabag to go over the split, tiny lick just to make it adhere, then dop nail glue / cyanoacrylate a tiny amount on top to soak through and adhere. let it dry, then you can trim the excess and even file it. If you do a lot of typing it will last until the split grows out