Given that the ratio of m to n is 13:11, we can write m = 13k and n = 11k for some constant k. Substituting these expressions into the given expression, we get:

\(\frac{m^2 - n^2}{(m + n)^2} = \frac{(13k)^2 - (11k)^2}{(13k + 11k)^2} = \frac{169k^2 - 121k^2}{(24k)^2} = \frac{48k^2}{576k^2} = \frac{1}{12}\)

So, the ratio of m\(^2\) - n\(^2\) to (m + n)\(^2\) is 1:12.