Find the sum of all integer values of n such that the equation \frac{x}{(y z)^{2}}+\frac{y}{(z x)^{2}}+\frac{z}{(x y)^{2}}=n has a solution in positive integers.
Find the sum of all integer values of n such that the equation \frac{x}{(y z)^{2}}+\frac{y}{(z x)^{2}}+\frac{z}{(x y)^{2}}=n has a solution in positive integers.