jmc

Because of Vieta's Formulas, if we know the coefficient of the $x^{2007}$ and $x^{2006}$ term, we can find the sum of all the roots. The coefficient of the $x^{2007}$ term is easy to find -- it's $1$. Using the Binomial Theorem in $(x-1{)}^{2007}$, the coefficient of the $x^{2006}$ term is $-\left(\genfrac{}{}{0ex}{}{2007}{2006}\right)+2=-2005$. Thus, by Vieta's Formulas, the sum of all $2007$ roots is $\frac{-(-2005)}{1}=\boxed{2005}$.