One die and 1, 2 or 3 coins

A fair die is tossed.
If the die lands on 1, 2 or 3, then 3 fair coins are tossed.
If the die lands on 4 or 5, then 2 fair coins are tossed.
If the die lands on 6, then 1 fair coin is tossed.

Given that the resulting coin tosses produced no tails, what is the probability that the die landed on 6?

The probability can be expressed as \( \dfrac ab\) for coprime positive integers \(a\) and \(b\), find the value of \(a+b\).

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