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Algebra Level 5

If \(a,b\in \mathbb{R}\) such that \[ E=\sqrt { { (a-b) }^{ 2 }+ (2-a-b )^{ 2 }+{ (2a-3b) }^{ 2 } } \] And If minimum value of \(E\) can be expressed as \( { E }_{ min }=\frac { m }{ \sqrt { n } } \) where \(m,n\) are integers such that \(n\) is a square free integer, then find the value of \(\displaystyle \mathrm{m + n}\).

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