Move yourself to four years back!

An integer \(x\) is selected at random between \(\displaystyle 1\) and \(2011!\). The probability that \(x^{x}-1\) is divisible by 2011 can be expressed in the form \(\dfrac{m}{n}\) where \(m\) and \(n\) are positive coprime numbers. Find the value of \(m\).

Details and Assumptions

You may use the fact that 2011 is prime.

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