How to rewrite kinetic mass balance to get to proper SI units?

Suppose from kinetic mass balance I get the following differential equation of the molarity substances $A$,$B$, and $C$ in a reactor, with molar in- or outflow rate $\phi$, and rate constant $k$:


$$
\frac{\mathrm{d}}{\mathrm{d}t}[C] 
= k[A]^2[B]^3 + \phi{C\_{\mathrm{in}}} - \phi{C\_{\mathrm{out}}}
$$


Where the dimensions convert to:


$$
[\pu{mol L-1 s-1}] 
= [\pu{s-1}] [\pu{mol5 L-5}] + [\pu{mol s-1}] - [\pu{mol s-1}]
$$


Which can be simplified by adding the flow rate terms to:


$$
[\pu{mol L-1 s-1}] 
= [\pu{s-1}] [\pu{mol5 L-5}] \pm [\pu{mol s-1}]
$$


By cancelling similar terms mole,seconds on both sides to:


$$[\pu{L-1}] = [\pu{mol4 L-5}] \pm 1$$


This seems that something is off about the rate constant, but also that there is no $\pu{L-1}$ term in the molar flow rate.


I don't expect exact answers to this, but could someone point me the right way, or send some clear explanation on either reaction rate constants or on kinetic mass balances? It seems I cannot find clear explanations, not even in textbooks.


