Don't Order The Same

Six guests sit around a circular table at a wedding reception. They each order one of three entrées: Salmon, Beef, or Lasagna. Each guest chooses their entrée independently at random, with each choice equally likely.

The probability that no two adjacent guests order the same entrées is \(\frac{a}{b},\) where \(a\) and \(b\) are coprime positive integers. What is \(a+b?\)

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