Let m be the largest real solution to the equation

\frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19}=x^{2}-11 x-4

There are positive integers a, b, and c such that m=a+\sqrt{b+\sqrt{c}}. Find a+b+c.

Let m be the largest real solution to the equation

\frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19}=x^{2}-11 x-4

There are positive integers a, b, and c such that m=a+\sqrt{b+\sqrt{c}}. Find a+b+c.