Given a positive integer \ell, define the sequence \{a^{(\ell)}_n\}_{n=1}^{\infty} such that a^{(\ell)}_n = \lfloor n + \sqrt[\ell]{ n} + \frac{1}{2} \rfloor for all positive integers n. Let S denote the set of positive integers that appear in all three of the sequences \{a^{(2)}_n\}_{n=1}^{\infty}, \{a^{(3)}_n\}_{n=1}^{\infty}, and \{a^{(4)}_n\}_{n=1}^{\infty}. Find the sum of the elements of S that lie in the interval [1, 100].