To solve the equation \( 27x^{3/4} - 1 = 26 \), we start by isolating \( 27x^{3/4} \):
\[ 27x^{3/4} = 26 + 1 \]
\[ 27x^{3/4} = 27 \]
Next, we can divide both sides by 27:
\[ x^{3/4} = 1 \]
Now, to eliminate the exponent \( \frac{3}{4} \), we raise both sides to the reciprocal power \( \frac{4}{3} \):
\[ x = 1^{\frac{4}{3}} = 1 \]
Thus, the solution for \( x \) is:
\[ x = 1 \]
Therefore, the correct answer is:
1