Let \(a\) be a real number and let \((4a+3)^4+(4a-1)^4=322\). If the positive solution for \(a\) can be expressed as \(\dfrac{n\sqrt{k}-x}{y}\), with \(n\), \(k\), \(x\) and \(y\) all co-prime positive integers, find \((n+k)^{y-x}\)

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