25. \( 6(x+4)^{\frac{1}{3}}-24=0 \)

To solve the equation \( 6(x+4)^{\frac{1}{3}}-24=0 \), let's start by isolating the cubic root term. First, add 24 to both sides: \[ 6(x+4)^{\frac{1}{3}} = 24 \] Next, divide both sides by 6: \[ (x+4)^{\frac{1}{3}} = 4 \] Now, to eliminate the cube root, cube both sides: \[ x + 4 = 4^3 \] \[ x + 4 = 64 \] Finally, subtract 4 from both sides to solve for \( x \): \[ x = 64 - 4 \] \[ x = 60 \] The solution is \( x = 60 \).