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

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 $\alpha + \beta$ .

The answer is 11.

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