Bertha has $ 6$ daughters and no sons. Some of her daughters have $ 6$ daughters and the rest have none. Bertha has a total of $ 30$ daughters and granddaughters, and no great-grand daughters. How many of Bertha's daughters and granddaughters have no daughters?

$ \textbf{(A)}\ 22\qquad
\textbf{(B)}\ 23\qquad
\textbf{(C)}\ 24\qquad
\textbf{(D)}\ 25\qquad
\textbf{(E)}\ 26$
1. Bertha has 6 daughters.
2. Let \( x \) be the number of Bertha's daughters who each have 6 daughters.
3. Therefore, the number of granddaughters is \( 6x \).
4. Bertha has a total of 30 daughters and granddaughters.
5. The equation representing the total number of daughters and granddaughters is:
   \[
   6 + 6x = 30
   \]
6. Solving for \( x \):
   \[
   6 + 6x = 30 \implies 6x = 24 \implies x = 4
   \]
7. So, 4 of Bertha's daughters have 6 daughters each.
8. The remaining daughters of Bertha who have no daughters are:
   \[
   6 - 4 = 2
   \]
9. All 24 granddaughters have no daughters.
10. Therefore, the total number of Bertha's daughters and granddaughters who have no daughters is:
    \[
    2 + 24 = 26
    \]

The final answer is \(\boxed{26}\).