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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