Helm Install Traefik - Define two Ingress Classes. One Public, one Private

Is it possible, with the helm installation, to configure more than one Ingress Class?

We have some services which should be served via a Public Load Balancer, and some services which should only be served with a Internal Load Balancer, but never both.

With ALB Controller, I would define this on the ingress definition itself, which the nginx controller I would have to install the helm chart twice.

Can anyone explain what my choices are here?