Roll Me A Square

Spongebob loves square numbers. So, he decides to keep rolling a fair six-sided die, until any consecutive substring represent(s) a perfect square less than 100. e.g. If his last two rolls were first a 2 and then a 5, he would be done since 25 is a perfect square. Or, for example, any time he rolls a 4 he would also be done since 4 is a square number.

If the expected number of rolls he must make is \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?

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