New Year's Countdown Day 30: Goodbye 2017

Algebra Level 4

20x+20x+20x+17303030=17 \large { \sqrt[30]{20x +\sqrt[30]{20x + \sqrt[30]{20x + 17}}} = 17 }

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

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