A parabola is defined parametrically by the following system of equations:

\(\begin{cases} x = (3t-1)(t-1)+\mathcal{C}_1\\ y = (2t+1)^2 + \mathcal{C}_2 \end{cases}\)

If the Latus Rectum can be expressed as \(\dfrac{a^p \times b^q}{c^r}\), where \(a,b,c\) are prime numbers, and \(p,q,r\) are positive integers, find the value of \(ap+bq+cr\)

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