# Rational Root Theorem won't save you this time

Algebra Level 5

Let $$r_1,r_2$$ be the two largest real roots of the polynomial $P(x)=3x^3-17x+5\sqrt{6}$

If $$r_1+ r_2$$ can be expressed as $\dfrac{\sqrt{a}+\sqrt{b}}{c}$ for positive integers $$a,b,c$$, then what is the smallest possible value of $$a+b+c$$?

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