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 \(a\) is an integer, \(b\) and is not divisible by the square of any prime. What is the value of \(a+b\) ?

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