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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