If $$(x+6)^3+(2x+3)^3+(3x+5)^3=(3x+18)(2x+3)(3x+5)$$, then what is the value of x?

$$(x+6)^3+(2x+3)^3+(3x+5)^3=(3x+18)(2x+3)(3x+5)$$

$$(x+6)^3+(2x+3)^3+(3x+5)^3=\left[3\left(x+6\right)\right](2x+3)(3x+5)$$

$$(x+6)^3+(2x+3)^3+(3x+5)^3-3\left(x+6\right)(2x+3)(3x+5)=0$$

This is in the form of $$a^3+b^3+c^3-3abc=0$$, where $$a\ne b\ne c$$ then $$a+b+c=0$$

$$\Rightarrow$$  $$\left(x+6\right)+\left(2x+3\right)+\left(3x+5\right)=0$$

$$\Rightarrow$$  $$6x+14=0$$

$$\Rightarrow$$  $$x=-\frac{7}{3}$$

Hence, the correct answer is Option C