To solve the equation, we need to simplify both sides and then solve for x.

Starting with the left side of the equation:

(7x - 11)^3

Using the formula for expanding a cube of a binomial, we have:

(7x)^3 - 3(7x)^2(11) + 3(7x)(11)^2 - (11)^3

Simplifying further:

343x^3 - 3(49x^2)(11) + 3(7x)(121) - 1331

Now, let's simplify the right side of the equation:

2^5 * 2^2 + 87^2

Using the properties of exponents:

32 * 4 + 7569

Simplifying further:

128 + 7569

= 7697

Now, we can set the two sides of the equation equal to each other:

343x^3 - 3(49x^2)(11) + 3(7x)(121) - 1331 = 7697

Combining like terms:

343x^3 - 1617x^2 + 2541x - 1331 = 7697

Rearranging the equation:

343x^3 - 1617x^2 + 2541x - 9028 = 0

At this point, we can either solve the equation by factoring, using the rational root theorem, or by using numerical methods such as graphing or using a calculator.