It is given that \(x+\dfrac{1}{x}=4\) and \(\dfrac{Ax^{2}}{x^{4}+x^{2}+1}=\dfrac{49}{750}\).

If the value of \(A\) can be expressed as \(\dfrac {m}{n}\), where \(m\) and \(n\) are coprime positive integers, what is the value of \(m+n\)?

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