To solve for \( c \) in the equation
\[ 69 = c^3, \]
we first rewrite the equation to isolate \( c \):
\[ c^3 = 69. \]
Next, we take the cube root of both sides to solve for \( c \):
\[ c = \sqrt[3]{69}. \]
Since 69 can be factored into its prime factors as \( 3 \times 23 \) and neither of these factors is a perfect cube, we cannot simplify \( \sqrt[3]{69} \) further. Thus, the answer in simplest radical form is
\[ c = \sqrt[3]{69}. \]
So, the solution is:
\[ \boxed{\sqrt[3]{69}}. \]
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