2019 AIME I Problem 12

Given f(z)=z^{2}-19 z, there are complex numbers z with the property that z, f(z), and f(f(z)) are the vertices of a right triangle in the complex plane with a right angle at f(z). There are positive integers m and n such that one such value of z is m+\sqrt{n}+11 i. Find m+n.