Answer
$12(6x+1)^{1/3}(4x-3)^{1/2}(5x-1)$
Work Step by Step
We simplify:
$6(6x+1)^{1/3}(4x-3)^{3/2}+6(6x+1)^{4/3}(4x-3)^{1/2}
=6(6x+1)^{1/3}(4x-3)^{1/2}[(4x-3)^{2/2}+(6x+1)^{3/3}]
=6(6x+1)^{1/3}(4x-3)^{1/2}[(4x-3)+(6x+1)]
=6(6x+1)^{1/3}(4x-3)^{1/2}(10x-2)\\
=6*2(6x+1)^{1/3}(4x-3)^{1/2}(5x-1)\\
=12(6x+1)^{1/3}(4x-3)^{1/2}(5x-1)$