The shortest distance might go the long way round!

Geometry Level 4

You are given a ice cream cone with radius 1 m and slant length of 4 m (I know it's huge!) . You start winding a thread around the cone from a point on the rim of the cone in such a way so that you reach the starting point in the shortest distance.

If the shortest distance is \(x\sqrt { y } \) for positive integers \(x \) and \(y\) with \(y\) square-free, find the value of \(x+y\).

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