Let f(x)=(x-5)(x-12) and g(x)=(x-6)(x-10). Find the sum of all integers n such that \frac{f(g(n))}{f(n)^{2}} is defined and an integer.
Let f(x)=(x-5)(x-12) and g(x)=(x-6)(x-10). Find the sum of all integers n such that \frac{f(g(n))}{f(n)^{2}} is defined and an integer.