An ant starts a random walk on the real number line at \(0\). At each step, the ant moves by \(+1\) or \(-1\) with equal probability. After \(6\) moves, the probability that the ant is on a positive number can be expressed as \(\dfrac{a}{b},\) where \(a\) and \(b\) are positive coprime integers. What is the value of \(a+b?\)

This problem is posed by Michael T.

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