Let $$x, y, z$$ be complex numbers such that $$\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}=9$$, $$\frac{x^{2}}{y+z}+\frac{y^{2}}{z+x}+\frac{z^{2}}{x+y}=64$$, and $$\frac{x^{3}}{y+z}+\frac{y^{3}}{z+x}+\frac{z^{3}}{x+y}=488$$. If $$\frac{x}{yz}+\frac{y}{zx}+\frac{z}{xy}=\frac{m}{n}$$ where $$m, n$$ are positive integers with $$\gcd(m,n)=1$$, find $$m+n$$.