Domain registering and invisible recaptcha issue

[Remitur]

I'm realizing an external html landing page that, using a form, allows the user to try to register a selected domain.

Submit button calls:

 mydomain.com/cart.php?a=add&domain=register&sld=domainname&tld=.com

The issue is that doing so, I'm getting a white page with just the message

{"result":{"error":"The characters you entered didn\u0027t match the image shown. Please try again."}}

Note: If I do the very same, but from a .php page inside WHMCS, it works quite good:

- if the user is asked for recaptcha compiling, everything works fine 

- if the user is not asked for recaptcha compiling, he gets just a quick message " The characters you entered didn't match the image shown. Please try again" that disappears immediately, and everything go on regularly...

Any idea on how to fix this recaptcha issue?

(By the way: there's any way to call /cart.php bypassing recaptcha request? I could move recaptcha from /cart.php to the first page...)