Welcome to the community, thanks for reaching out.
I am very sorry to hear that you are unable to receive any audio from the left channel in your QuietComfort 35 headphones.You have stated that by wiggling the headphones you will once again receive audio, this would indicate that there is damage to the audio channel. However, I would like to offer some troubleshooting to determine whether or not this is the case.
Does this occur with both a wired and a Bluetooth connection?
Can you test your headphones with another device to see if this issue persists?