Dice Rolls

A single die is rolled until a run of six different faces appears. For example,one might roll the sequence 535463261536435344151612534 with only the last six rolls all distinct. The expected number of rolls to attain this can be written as \(\frac{a}{b},\) where \(a\) and \(b\) are positive coprime integers. Find \(a+b.\)

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