A sphere intersects the $xy$-plane in a circle centered at $(2,4,0)$ with radius 1.  The sphere also intersects the $yz$-plane in a circle centered at $(0,4,-7),$ with radius $r.$  Find $r.$The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

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