A unit square \(ABCD\) has two points \(M,N\) inside it (possible on the perimeter) such that \(\overline{MA} + \overline{MB} + \overline{MC} + \overline{NA} + \overline{ND} + \overline{NC} \) is a minimum.

If \( \overline{MN} = \frac {\sqrt a }{b} \), then what is the value of \(a+b\)?

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