Let's deal with the CPU cooling system first, even though you say the problem appears to be the CASE fans. There is a single cable to go from the PUMP unit of that AIO system to the CPU_FAN header, and it just sends the pump speed signal to that header. Then there's a cable to go from a socket on the side of the pump to a mobo USB2 header. This is how the Armoury Crate software utility communicates with the AIO system. IT is what controls the speed of the rad fans. Those two fans are to be plugged into outputs attached to the pump. And of course, the pump has a cable with a wide connector that plugs into a SATA power output from the PSU.
Your four Corsair LL120 fans are plugged into mobo headers I gather - probably one fan per header. There are six such SYS_FAN headers. See your mobo manual p. 47 for how to enter BIOS Setup. You will get either the EZ Mode display (p. 50) or the Advanced Mode (p. 53). Either way, clock on the Hardware Monitor block to get to its Menu on p. 62. Go to p. 63 to make adjustments. Each fan header is adjusted separately, although you want all four of your headers in use to be configured the same. Choose a header (say, SYS_FAN1) at the top. As a first set, click on All Set Default at bottom centre. Now look at that graph with 4 blue dots. point and hold down the mouse key to drag the bottom left dot to a higher speed. Do the same for the next dot over. You have just told it to use those as the lowest speeds for the coldest temperatures, and set them faster than the original defaults. Now, choose another SYS_FAN header and do exactly the same. Repeat until all the headers you have fans plugged into have been adjusted. Then press the F10 key to pop up an Exit Menu. You will need to SAVE and REBOOT your system. The new fan speed settings will take over and should prevent any case fan from being told to run so slow it stalls.