iPhone 11 Pro Max not coming on after charging

Try a "forced" restart of your 11, using these gestures:

Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the side (power) button. Only when the Apple logo appears (it might take 10-20 seconds), release that button (ignore all other screens that might appear, the one with the "slider" to turn the device off included).

If the issue persists, it might be a hardware (battery? charging port? other internal component?) failure but we, just users like you, cannot diagnose that issue remotely, sorry.

I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.

iPhone won’t turn on:

• Charge the device for up to one hour.
• Click ▶︎ Force Restart iPhone for detailed instructions.

Need more help?

• Chat now or call 1-800-APLCARE.
• International Support.

Click ▶︎ iPhone User Guide. 📖