The Cube Root of \(i\)?

Algebra Level 2

First, you can read about the definition of \(i\), Imaginary Unit in the Algebra Glossary


\(\sqrt[3]{\strut i}=\displaystyle \frac{\sqrt{a}+i}{b}\)

where \(a\) and \(b\) is positive integers and \(a\) is not a square number.

What is the value of \(a+b\)?

This problem is inspired by The Square Root of \(i\)?


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