Surd Problem 2

Algebra Level 5

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

2313=x3+y3+z3 \sqrt[3]{\sqrt[3]{2}-1} = \sqrt[3]{x}+\sqrt[3]{y}+\sqrt[3]{z}

If x+y+z x+y+z can be expressed as mn \dfrac{m}{n} , where m m and n n are relatively prime positive integers,

find m+n m+n .

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