y=x(1-x)^(1/3)

The derivative of the function turns out to be (1-x)^(1/3) - x/(3(1-x)^2/3)

Using the calculator I found out the max is 0.750, .472...But when I set the derivative equal to 0...and tried to factor I got x=-3/11, x=1...I understand how to find the mix and max, my question is how to factor this particular equation...