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.