Let $$x, y$$ be real numbers such that $$xy=1$$. Let $$T$$ and $$t$$ be the largest and the smallest values of the expression $$\frac{(x+y)^{2}-(x-y)-2}{(x+y)^{2}+(x-y)-2}$$. If $$T+t$$ can be expressed in the form $$\frac{m}{n}$$ where $$m, n$$ are nonzero integers with $$\gcd(m,n)=1$$, find the value of $$m+n$$.