Find the positive integers $n$ that are not divisible by $3$ if the number $2^{n^2-10} + 2133$ is a perfect cube. 

Solve the Diophantine equation $x^3 = 2^{n^2-10} + 2133$ where $x, n \in \mathbb{N}$ and $3 \nmid n$.

Let's think step by step and output the final answer within \boxed{}.
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