Find the region R bounded by the graphs $\displaystyle y = x^3$ and$\displaystyle y = x+ 6$

The left curve $\displaystyle y=x+6$ becomes $\displaystyle x= y-6 $

The right curve $\displaystyle y=x^3$ becomes$\displaystyle x=y^{1/3}$

How do I find the intersection point of the curve and the root which will be the pper and lower boundaries. The book says I can use synthetic division to find the roots.