how long will it take for my hair to grow?

recently as in today, I cut about 3-5 inches of my hair off. i am not 100% black, but more african american than anything else. I have very thick and curly hair that came down way past my chin, i'd say it was 10-11 inches. i cut it due to my tips being damaged from exessive box dye. i deep conditioned with devacurl one condition and applied olive oil, Jamaican black castor oil, olive oil leave in conditioner, along with taking a 10000mg biotin pill. i plan on repeating this process until my length reaches atleast 8-9 inches again. my hair is now 5-6 inches approximate & reaches the tip of my nose when i pull it down. how long will it take to grow back?