JEE (Advanced) 2019 Paper-2 Question 42

Question 42

For $$a \in R, |a| > 1,$$ let
$$\lim_{n \rightarrow \infty} \left(\frac{1 + \sqrt[3]{2} + ... + \sqrt[3]{n}}{n^{\frac{7}{3} \left(\frac{1}{\left(an + 1\right)^2} + \frac{1}{\left(an + 2\right)^2} + ... + \frac{1}{\left(an + n\right)^2} \right)}}\right) = 54.$$
Then the possible value(s) of a is/are



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