Find the sum of all roots, real and nonreal, of the equation
\[x^{2001}+\left ( \frac{1}{2}-x\right) ^{2001}=0\]
given that there are no multiple roots.
Source AIME 2001
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin