When the value of the sum \(\displaystyle\sum_{n=1}^{\infty} \biggl( n \cdot \dfrac{3^{n-1} \cdot 2}{5^n}\biggr)\) is expressed in the form \(\dfrac{a}{b}\) for relatively prime positive integers \(a\) and \(b\), what is the value of \(a+b\)?

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