\[\large f(x)=\dfrac1{x^2}\int_x^{x+6}\sqrt{5t^4+1}\,dt\]

If \( \displaystyle \lim_{x\to\infty} f(x) = \alpha \sqrt{\beta} \), where \(\alpha\) and \(\beta\) are positive integers with \(\beta\) square-free, write your answer as \(\alpha + \beta\).

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