Finding The Minimum Value

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

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