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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