Find the sum of all the roots, real and non-real, of the equation x^{2001}+\left(\frac{1}{2}-x\right)^{2001}=0, given that there are no multiple roots.
Find the sum of all the roots, real and non-real, of the equation x^{2001}+\left(\frac{1}{2}-x\right)^{2001}=0, given that there are no multiple roots.