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Find \[ \lim_{x \to \infty} \frac{ \sqrt{ x^{2} +1} - (x^{3} +1)^{ \frac{1}{3} } }{ (x^{4} +1)^{ \frac{1}{4} } -(x^{4} +1)^{\frac{1}{5} } } +1 \]

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