Writing PDE in the form of convervation law

Question

What does one need to know in order to write $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+\frac{\partial^3 u}{\partial x^3}=0$ in the form of a conservation law, which contains the flux? I was thinking about the Burger's equation $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=D\frac{\partial^2 u}{\partial x^2}$, where the flux $\phi = -D\frac{\partial u}{\partial x}+Q(u)$, and $Q(u) = u^2$, but this does not seem "applicable enough" due to the third derivative of $u$ in the equation. I'd appreciate some hints.