The sum of all real numbers $x$ such that

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

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

This problem is posed by Zi Song Y.

**Details and assumptions**

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

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