How find box arests based only in volume

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I'm trying to figure how I can find the dimensions of a box based only on the volume. Lets imagine I have a box with:

height: 13 cm
width: 6 cm
lenght: 8 cm

Using the volume formula ($v=l*h*w$) I get 624 $cm^3$ as volume. However what I want is the contrary, I have the volume and I want find the edges. I've made the following suppositions:

height: x
width: x+n
length: x+k

$$v=x^3+x^2(n+k)+xkn$$

so if my volume is 624 $cm^3$, how can I solve this?

$$x3+x2(n+k)+xkn=624$$