# Surd Problem 2

Algebra Level 5

$$x$$, $$y$$ and $$z$$ are rational numbers such that

$\sqrt[3]{\sqrt[3]{2}-1} = \sqrt[3]{x}+\sqrt[3]{y}+\sqrt[3]{z}$

and $$x+y+z = \frac{m}{n}$$ where $$m$$ and $$n$$ are coprime positive integers.

Find the value of $$m+n$$.

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