Normally once your router (RUTX11) is connected to "other" WiFi as a client, you should be able to get internet access on your RUTX11 LAN/WiFi clients.
Could you please check whether there is an IP conflict between your RUTX11 LAN network and the "other" WiFi network? if both are using the same subnet (ex: 192.168.1.0/24), that could be the root of this issue.
To work this out, you might need to try one of the following solutions :
1- Enable WiFi WAN on your RUTX11:
You can use this if you want to isolate your LAN network and use "other" only as a WAN source. Here is a video that shows how to change your LAN Network address and enable WiFi WAN on your router: How to Enable WiFi WAN on Teltonika Networks Routers
2- Configure your RUTX11 to work on relay mode:
This works as a relayed extension of "other" WiFi network and your clients will be directly connected to it. Please follow the instructions in this Wiki article to configure relay mode on your router: https://wiki.teltonika-networks.com/view/Relayd_RutOS