Consider the set $E = \{5, 6, 7, 8, 9\}$. For any partition $\{A, B\}$ of $E$, with both $A$ and $B$ non-empty, consider the number obtained by adding the product of elements of $A$ to the product of elements of $B$. Let $N$ be the largest prime number among these numbers. Find the sum of the digits of $N$.

Let's think step by step and output the final answer within \boxed{}.
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