Evaluate the integral
\[
\int x^{6}\left(x^{7}-11\right)^{28} d x
\]
by making the appropriate substitution: $u^{\prime}=$
\[
\int x^{6}\left(x^{7}-11\right)^{28} d x=
\]
NOTE: Your answer should be in terms of $x$ and not $u$.

Step 1 ：Let's start by making the substitution $u = x^7 - 11$. This gives us $du = 7x^6 dx$.

Step 2 ：However, our integral has $x^6 dx$, not $7x^6 dx$. To correct for this, we can multiply and divide by 7 inside the integral. This will give us $\frac{1}{7} \int 7x^6 (x^7 - 11)^{28} dx$.

Step 3 ：After the substitution, this can be rewritten as $\frac{1}{7} \int u^{28} du$.

Step 4 ：Integrating this gives us $\frac{1}{7} \cdot \frac{u^{29}}{29} + C = \frac{u^{29}}{203} + C$.

Step 5 ：Substituting $u$ back in terms of $x$, we get $\frac{(x^7 - 11)^{29}}{203} + C$.

Step 6 ：\(\boxed{\frac{(x^7 - 11)^{29}}{203} + C}\) is the final answer.