\textbf{111.} Find the range of the function $f(x) = 2^{\frac{1}{3}\sqrt{9\cos^2(x)-1}} - 2^{\frac{1}{3}\sqrt{1-9\cos^2(x)}}$ in the form $[a, b]$. The value of $b - a$ is:
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(1) $\dfrac{9}{5}$ \hfill (2) $\dfrac{15}{4}$ \hfill (3) $\dfrac{9}{2}$ \hfill (4) $\dfrac{21}{4}$
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