What do you mean by broke? If there is a chip in a slot, you can also try to do a patch. Now a luthier would not do this (and it is not the right thing to do), but that said, you can take super glue, mix it with baking power and fill in the chiped portion of the nut. This will harden to a white solid, that you can reshape and file.
I have used this method to reslot a string grove (like if it was too low or if I didn't like the spacing). However, using a luthier to do it right is much better. Also, if you choose to mess with the super-glue method, put some masking on either side of the nut, so you do not cause more trouble than it's worth.
ˇpapá gordo ain’t no madre flaca!
'20 A3, '84 1N, '84 A5-1, '06 Phoenix Bluegrass, 2012 Cohen A5, 2012 Muth A5