2010 AIME I Problem 9

Let (a, b, c) be a real solution of the system of equations

& x^{3}-x y z=2 \\ & y^{3}-x y z=6 \\ & z^{3}-x y z=20

The greatest possible value of a^{3}+b^{3}+c^{3} can be written in the form \frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.