Marble Bag

A bag contains \(3\) red marbles, \(4\) blue marbles, \(6\) yellow marbles, and \(6\) green marbles. Four marbles are randomly drawn from the bag, without replacement. The probability of drawing a red, then blue, then green, and finally another red marble is \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. What is the value of \(a+b\)?

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