Because we live in a country that's dominated by its culture, and we all live by this culture, we have learned to absorb its values, to a greater or a lesser degree. What are the values?

Your question seems to ask what are the values of the American culture. This is an assumption based on when you write that, "we live in a country" and "we absorb its values."
This said, read the words of Thomas Jefferson on the drafting of the Bill of Rights. On this, his words were:


"[A] bill of rights is what the people are entitled to against every government on earth, general or particular, and what no just government should refuse."       - Thomas Jefferson, December 20, 1787


This is the first step to understand American values. The founding generation was looking for a way to guarantee rights and liberties that will ensure "liberty and justice for all" as it is stated in the Pledge of Allegiance. Coming from a place where persecution and division were the norm, the new Americans were hungry, not just for freedom, but also for opportunities to succeed, for personal validation, and for the recognition that they went out of their way to make these goals happen.
Therefore, it is safe to say that American values, at least the original values upon which the Constitution and the Bill of Rights were drafted, are found in these historical documents and can be easily extrapolated, which we will, for your answer. These values are still summoned to this day and, interestingly enough, many people still abide by them. They are:
Equal Opportunity (a.k.a "with liberty and justice for all")
The right to Achievement and Success

The right to material comfort
The option for Activity and Work

Practicality and Efficiency
Progress
Science
Democracy and Enterprise
Freedom
ALSO SEE: John J. Macionis (2005) Sociology. 10th ed. Upper Saddle River, New Jersey: Pearson Prentice Hall. p. 66 for more information.