Answer: \(x=1.4\).

Rewrite the equation as a standard quadratic in the chosen variable, then solve and reject any value that does not satisfy the original form.

Let

\(u=x^{2/3}\).

Then

\(x^{-2/3}=\frac1u\).

The equation becomes

\(12u-\frac5u-11=0\).

Multiply by \(u\):

\(12u^2-11u-5=0\).

Factorise:

\((3u+1)(4u-5)=0\).

So

\(u=-\frac13\) or \(u=\frac54\).

But \(u=x^{2/3}\), and since \(x\gt 0\), \(u\gt 0\). Therefore

\(u=\frac54\).

So

\(x^{2/3}=\frac54\).

Raise both sides to the power \(\frac32\):

\(x=\left(\frac54\right)^{3/2}\).

Numerically,

\(x\approx1.3975\).

Correct to one decimal place,

\(x=1.4\).