A father and his son can finish digging a well if the father works for 6 hours and his son for 12 hours, or they can finish digging if the father works for 9 hours and his son 8 hours.. It will take for them \(\dfrac ab\) hours to finish digging if they work together.

If \( a\) and \(b\) are coprime positive integers, find \(a+b\).

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