Let \(X\) be the number of distinct possibilities for the units digit of a perfect cube when written in base \(18815\). Find the last three digits of \(X\) (in decimal base).

**Details and assumptions**

The prime factorization of \(18815\) is \(18815= 5 \times 53 \times 71\).

We're talking about \(18815\) in its decimal representation.

This problem is similar to this one.

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