That's a lot of squares

\[\displaystyle \sum _{ j=0 }^{ 100 }{ {\binom{100}{j} }^{ 2 } } = \binom{m}{n} \]

If \(m,n\) are positive integers that satisfy the equation above, determine the minimum value of \(m+n\).

Image Credit: Wikimedia R. A. Nonenmacher
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