Growing out dyed hair

My natural hair is light/medium brown but I have dyed it black for several years. I decided 6 months ago that I want to go back to my natural color so the last time I dyed it was 6 months ago.

However my roots haven’t grown that much my hair still looks the same just a bit lighter at the top! I have been for a hair cut but I don’t want to go too short (it’s shoulder length now.) how long will this process take? Obviously when my natural hair gets to a certain length I will just chop off all the dyed hair.