If \(x+\dfrac 1x = \sqrt{58}i\), then it can be proven that \(\sin (x^2) + \sin \left(\dfrac 1{x^2}\right) + \cos (m) = 0\), where \(m\) is a positive integer. Find the value of \(\cos(m+2)\).

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**Notation:** \(i = \sqrt{-1}\) denotes the imaginary unit.

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