yes, you can find the cube root of a negative and it will be a negative number. Think of it like this.
55 =25
-5x-5=25
BUT
-5x-5x-5x= -125
The cube root of -125 is -5.
This happens because multiplying 2 negatives together gives you a positive, then you multiply that positive number by a negative and get the final result as a negative number!