Alright, let's solve the equation step by step:
Given the equation:
[tex]\[ 1331x^3 - 216 = 0 \][/tex]
First, we need to isolate [tex]\(x^3\)[/tex]:
[tex]\[ 1331x^3 = 216 \][/tex]
Next, divide both sides of the equation by 1331 to solve for [tex]\( x^3 \)[/tex]:
[tex]\[ x^3 = \frac{216}{1331} \][/tex]
Now, we need to solve for [tex]\(x\)[/tex] by taking the cube root of both sides.
[tex]\[
x = \sqrt[3]{\frac{216}{1331}}
\][/tex]
After calculating the value, we find:
[tex]\[ x = 0.5454545454545455 \][/tex]
Recognizing this as a common fraction, we can express this decimal in a simplified fraction.
[tex]\[ 0.5454545454545455 = \frac{6}{11} \][/tex]
So, the value of [tex]\(x\)[/tex] is:
[tex]\[ \boxed{\frac{6}{11}} \][/tex]
Thus, the correct answer is:
D. [tex]\(\frac{6}{11}\)[/tex]
