Zi Song's Gargantuan Root

Algebra Level 5

The sum of all real numbers xx such that

x=129(329x12013)x = \frac{1}{29}(3 - \sqrt[2013]{29x - 1})

can be written as abc\frac{a\sqrt{b}}{c}, where aa and cc are positive coprime integers and bb is a positive integer that is not divisible by the square of a prime. Find a+b+ca + b + c.

This problem is posed by Zi Song Y.

Details and assumptions

Note: a,ba, b and cc could be 1. For example, if the sum is 1=111 1 = \frac{1 \sqrt{1} } {1} , then your answer is a+b+c=3a+b+c = 3 .

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