These numbers... something isn't right

Algebra Level 5

Given that \(x\) is real, the minimum value of \(\sqrt { 1681{ x }^{ 2 }+16 } +\sqrt { (17-41x)^{ 2 }+25 } \) can be expressed in the form \(a\sqrt { b } \) where is \(b\) is square-free and \(a\) is a positive integer. Find \(a+b\).

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