Find the minimum possible value of
\[\sqrt{58 - 42x} + \sqrt{149 - 140 \sqrt{1 - x^2}}\]where $-1 \le x \le 1.$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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