How long will it take dyed hair to grow?

Okay so my natural hair is REALLY DARK BROWN, my hairs been highlighted for about 3 years, so it was a kinda bronze color. Then i bleached it plat blonde, hated it, so i went to that goldish color again. I just got nearly ALL of my spilt ends cut off, and was wondering how long will it take my dyed hair to grow now, My familys hair grows really fast