# Factorization is an art (3)

Algebra Level 4

$\large(64^{x}-128)^{3} + (128^{x}-64)^{3} = (128^{x}+64^{x}-192)^{3}$

If the sum of all real root(s) of the above equation is $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, and $$a+b = c^2$$, find $$|c|$$.

Notation: $$| \cdot |$$ denotes the absolute value function.

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