Let $z$ be a complex number such that
\[z^3 + \frac{1}{z^3} = 52.\]Find all possible values of
\[z + \frac{1}{z}.\]Enter all possible values, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $z$ be a complex number such that
\[z^3 + \frac{1}{z^3} = 52.\]Find all possible values of
\[z + \frac{1}{z}.\]Enter all possible values, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4, -2 + 3i, -2 - 3i
Let $z$ be a complex number such that
\[z^3 + \frac{1}{z^3} = 52.\]Find all possible values of
\[z + \frac{1}{z}.\]Enter all possible values, separated by commas.
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