Let $L >0$ be a constant and consider the random variables $\left(x_i\right)_{i=1}^n$ that follow a binomial distribution as $x_{i} \backsim \operatorname{Bin}(n,\frac{k}{n})$, but they are not necessary independent from each other. The variables $k$ and $n$ are integers.
I would like to know if there is a way to compute the following probability:
$$\mathbb{P}\left(\sum_{i=1}^n x_i^{-3}>L\right)$$
I can think about Azuma theorem but it was given for $\mathbb{P}\left(\sum_{i=1}^n x_{i}>L\right)$.
Thank you.