Answer: \(x=1.62\) or \(x=-1.97\).

Work through the given conditions step by step, keeping exact values until the final answer is required.

Let

\(u=x^{\frac35}.\)

Then the equation becomes

\(6u+1=\frac{12}{u}.\)

Multiplying by \(u\),

\(6u^2+u-12=0.\)

Factorise:

\((3u-4)(2u+3)=0.\)

So

\(u=\frac43\quad\text{or}\quad u=-\frac32.\)

Since \(u=x^{3/5}\),

\(x=\left(\frac43\right)^{5/3}=1.62\ldots,\)

or

\(x=-\left(\frac32\right)^{5/3}=-1.97\ldots.\)

Therefore, to 2 decimal places,

\(x=1.62\quad\text{or}\quad x=-1.97.\)

This gives the required answer: \(x=1.62\) or \(x=-1.97\).