( ∛3x+5 ) + 4 = 0

Answer 1

third root ( 3 x ) + 5 + 4 = 0

third root ( 3 x ) + 9 = 0

third root ( 3 x ) = - 9

93 x = - 9 ^ 3

3 x = - 729 Divide both sides by 3

x = - 729 / 3

x = - 243

Answer 2

If your expression mean :

third root ( 3 x + 5 ) + 4 = 0

then

third root ( 3 x + 5 ) = - 4

3 x + 5 = - 4 ^ 3

3 x + 5 = - 64

3 x = - 64 - 5

3 x = - 69 Divide both sides by 3

x = - 69 / 3

x = - 23