11's remainders

Let \(\displaystyle S_1=\sum_{n=6}^{10} (2n+1)^{n-5}\) and \(\displaystyle S_2=\sum_{n=6}^{10} (2n)^{n-5}\).

When \(S_1\) and \(S_2\) are divided by 11, they leave remainders \(a\) and \(b\) respectively.

Find the remainder when \(a^4b^4\) is divided by 11.

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