3, 2, 1 blast off

Algebra Level 5

We have the identity

\[ 3 \sqrt[3]{ \sqrt[3]{2} -1 } = \sqrt[3] {a} + \sqrt[3]{b} - \sqrt[3]{c}, \]

where \(a\), \(b\) and \(c\) are positive integers. What is the value of \( a + b + c \)?

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