Find all numbers $x$ satisfying $x^3 \equiv 1 \pmod A$.

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Given any two numbers $M,N \in \{1,2,\ldots,10^{18}\}$, find all numbers $x$ lying between $M$ and $N$ satisfying $$x^3\equiv1 \pmod A,$$ where $A$ can be any number.

I know the case when A is even. I want to calculate when A is odd.