Evaluate \[ \large \sum_{n=1}^{\infty}\dfrac{1}{\binom{2n}{n}}\]

If the answer can be expressed as \(\dfrac{a+b\sqrt{c}\pi}{d}\), where \(a,b,c\) and \(d\) are positive integers, \(c\) is square-free, and \(d\) is minimal, then find \(a+b+c+d\).

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