Kissing Spheres

Geometry Level 5

Given four congruent spheres, where each sphere is externally tangent to the other three spheres, a larger sphere, with a radius 1, contains all four spheres and the four spheres are all internally tangent to the larger sphere. The radii of the four congruent spheres can be expressed as \(-m+\sqrt{n}\). What is \(m+n\)?

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