If the extreme values of the function \( f(x) = (2\sqrt{6}+1)\cos x + (2\sqrt{2}-\sqrt{3})\sin x - 6 \) are m and M, then \( \sqrt{|M^2-m^2|} = \)
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For any function of the form \(f(x) = a\cos x + b\sin x + c\), the range is \( [c - \sqrt{a^2+b^2}, c + \sqrt{a^2+b^2}] \). The term \( \sqrt{a^2+b^2} \) represents the amplitude of the sinusoidal part.