100,000 points problem

Algebra Level 4

Let \(m\) be the the largest real solution to the equation

\[\dfrac{3}{x-3}+\dfrac{5}{x-5}+\dfrac{17}{x-17}+\dfrac{19}{x-19}=x^2-11x-4\]

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

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