# Happy Holiday

Algebra Level 4

Given that one of the root of $$f(x) = x^5+9x^4+7x^3+16x^2+6x+7$$ can be expressed as:

$-a-7\sqrt[3]{\dfrac{2}{b-3\sqrt{c}}} - \sqrt[3]{\dfrac{b-3\sqrt{c}}{2}}\$

for positive integers $$a,b$$ and $$c$$. Calculate $$a+b+c+1$$.

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