Conexant modems generally use proprietary
conexant drivers, available from conexant.
(You have to pay for the latest version, but there are older versions
still around for free.)
I have a suspicion that it may even work with the smartlink driver + alsa.
It is frustrating to install OS after OS in the hope that just
one will run your hardware - then to find that none of them would will... not out of the box. (Modems are an old bugbear.)
Usually it is best to google around the topic... enter your hardware as listed by lspci along with "linux" and you will find loads of discussions.
For modems, the one-stop shop is the linmodem project. Use the "scanmodem" script to discover what is known about your modem and where to look for support. It will over-inform you but you will learn loads.
Once you are done, would you enter your laptop in the HCL please?