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The surface area of a cone can be found using the formula S = πr(r + l), where r is the radius of the base and l is the slant height.
Plugging in the given values, we have S = π(6)(6 + 11) ≈ π(6)(17) ≈ 101.86 square units.
Therefore, the surface area of the cone is approximately 101.86 square units.