On UNO, when serial.print to UART pin 11, nothing comes out of pin 11
Of course it's only coming out on the serial monitor - you are printing it to the hardware UART which comes out on the serial monitor.

You have created a SoftwareSerial object which you are then completely ignoring and then using the HardwareSerial UART object instead, which is on pins 0/1.

If you want to use a SoftwareSerial object you should actually use the SoftwareSerial object.

Replace all the references to Serial with mySerial instead.