Find all integer solutions of the equation:

\[
\left\lfloor \frac{x}{1!} \right\rfloor + \left\lfloor \frac{x}{2!} \right\rfloor + \cdots + \left\lfloor \frac{x}{10!} \right\rfloor = 1001.
\]

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