Three mutually tangent spheres of radius \(1\) rest on a horizontal plane. A sphere of radius \(2\) rests on them. Find the distance from the plane to the top of the larger sphere, expressed in the form \(3 + \frac{\sqrt{x}}{y}\). Please find the value of \(x + y\).

Let's think step by step and output the final answer within \boxed{}.
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