# 100,000 points problem

Algebra Level 5

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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