# New Year's Countdown Day 30: Goodbye 2017

Algebra Level 4

$\large { \sqrt[30]{20x +\sqrt[30]{20x + \sqrt[30]{20x + 17}}} = 17 }$

Let $$N$$ be the sum of all the real solutions to the above equation. If $$N = \dfrac{a^b-a}{c},$$ where $$a,$$ $$b,$$ and $$c$$ are positive integers and $$a$$ and $$c$$ are coprime, then what is $$a+b+c?$$

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