If we consider that $1/6$ in place of $1/12$ mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will:

1. The definition of atomic mass unit ($1\text{amu}$) and Avogadro's number ($N_A$) are linked.2. If the definition of $1\text{amu}$ changes, the value of $N_A$ changes such that the mass of $1$ mole of a substance (in grams) remains numerically equal to its atomic/molecular mass.3. The actual mass of one mole of a substance is a physical quantity. If we change the unit "mole" (by changing the reference), the mass contained in "one mole" stays the same because the physical scale of atomic masses hasn't changed.