An equilateral triangle has sides of length $x+5, y+11$, and 14 . What is the value of $x+y$ ?

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In an equilateral triangle, all sides are of equal length. This means $x+5=14$ and $y+11=14$.

Solving these equations for $x$ and $y$, respectively, we get $x=14-5=9$ and $y=14-11=3$. Therefore, $x+y=9+3=12$.