A new Apéry-like series for ζ(11) derived via central difference operators

$$\begin{aligned}\zeta(11) = &\ \frac{45}{2} \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^{11} \binom{2n}{n}}- \frac{2079}{16} \sum_{n=1}^{\infty} \frac{(-1)^{n-1} H_n}{n^{10} \binom{2n}{n}} \\&+ \frac{4455}{64} \sum_{n=1}^{\infty} \frac{(-1)^{n-1} H_n^{(2)}}{n^9 \binom{2n}{n}}- \frac{1485}{128} \sum_{n=1}^{\infty} \frac{(-1)^{n-1} H_n^{(3)}}{n^8 \binom{2n}{n}} \\&+ \frac{99}{256} \sum_{n=1}^{\infty} \frac{(-1)^{n-1} H_n^{(4)}}{n^7 \binom{2n}{n}}\end{aligned}$$where $H_n^{(m)} = \sum_{k=1}^{n} k^{-m}$ are the generalized harmonic numbers.