I dyed my hair black for a few years when I was younger, and I had to cut it off. My hair is a few ticks lighter than black, so the grow-out wasn't that noticeable.
Generally, going and having the color professionally stripped out is the safest and best way to get the black out. It can fry your poor hair. I tried everything home wise to get the black out. Then it was blond and when I put brown over it, all the color eventually faded to orange.
If you want you natural color to come back, you might have to bite the bullet and let it grow and rock a short hair style for a few months. Roots are annoying, but the result is totally worth it.