2001 AIME I Problem 3

Find the sum of the roots, real and non-real, of the equation x^{2001}+\left(\frac 12-x\right)^{2001}=0, given that there are no multiple roots.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.