I’m answering my own question because I wanted to know how to solve the problem while using the new slapd.d/dynamic/cn=config backend and I didn’t wanted going back to the slapd.conf method.

When I try to add the new schema using ldapadd, I was always getting the following error:

ldapadd -H ldap://whatever.test.com -D "cn=admin,dc=whatever,dc=test,dc=com" -x -W -f mozillaabpersonalpha.ldif
ldap_add: Insufficient access (50)

So the BindDN I was using does not have that privileges. I would need to setup an ACL or to use the rootDN for that operation.

I don’t know why, but when configuring the slapd debian package, it allowed me to create an admin account for my on DIT, but it mentioned nothing about the rootDN. After some browsing, I found this Blog that explains how to set the password of the rootDN while using the cn=config schema.

So, edit the file 

/etc/ldap/slapd.d/cn=config/olcDatabase\=\{0\}config.ldif

 and add the following:

olcRootDN: cn=admin,cn=config
olcRootPW: mypassword

I had to restart the slapd for the changes to take effect (It shouldn’t be necessary, but …). In order to test it, I ran the following command:

ldapwhoami -H ldap://whatever.test.com -D "cn=admin,cn=config" -x -w mypassword

And it worked! The next step was to load the mozillaAbPersonAlpha schema in ldif format using ldapadd:

ldapadd -H ldap://whatever.test.com -D "cn=admin,cn=config" -x -w mypassword -f mozillaabpersonalpha.ldif

The response was successful