Happy Birthday World, Mankind, or Both?

Many Rabbis teach that Rosh Hashanah is the birthday of mankind. Many others teach that Rosh Hashanah is the birthday of creation. Some Rabbis (such as Rabbi Yitzchak Botton) teach (or at least mention) that Rosh Hashanah is the celebration of the birthday of both: that is 

1. all of creation AND

2. humankind. 

Since we know that the Creation of Creation began on day one and the Creation of Mankind occurred on day six, a single day seemingly cannot celebrate both events. This contradiction must have an answer. How can we reconcile the seeming disparity?

First Things First: Holy Wisdom