A Minimum value sum

Algebra Level 4

The minimum value of \[\sqrt{x^4 - x^2 - 24x + 145} + \sqrt{x^4 - 23x^2 - 2x + 145}\] can be expressed in the form \(a\sqrt{b}\) , where \(a\) and \(b\) are integers, with \(b\) is not divisible by the square of any prime. What is the value of \(a+b\) ?

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