# Not The Brute Force Approach

Algebra Level 5

Let $$m$$ be the largest real solution to the equation $\frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19}= x^2-11x-4.$

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

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