Triangles Are Important Here

\[ \large \dbinom{2n+1}3 = \dbinom{2n+2}n - \dbinom{2n+1}4 \]

Let \(a>1\) and \(b>1\) be the two solutions satisfying the equation above. What is the value of \(a+b\)?

\[ \]

Notation: \( \dbinom MN \) denotes the binomial coefficient, \( \binom MN = \dfrac{M!}{N!(M-N)!} \).

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