I was using a hex wrench with a ball end like this



to try to remove a steerer clamp bolt on a Thomson Elite stem.

The ball part of the wrench snapped off and is now stuck in the head of the bolt, and I can't get it out.

I can't grab it with a needlenose, because the broken piece is flush with the top of the bolt. There's nothing to grab. I tried drilling into the piece of wrench in the hopes of pulling it out once a bit was in it, but the bit won't drill into the tough steel.

Any advice?