The volume of the metal is equal to the difference between the final volume of water and the initial volume of water:

$$V_{metal} = V_{final} - V_{initial}$$

$$V_{metal} = 28.69 \ ml - 21.76 \ ml = 6.93 \ ml$$

Step 2: Calculate the density of the metal.

The density of the metal is equal to its mass divided by its volume:

$$\rho_{metal} = \frac{m_{metal}}{V_{metal}}$$

$$\rho_{metal} = \frac{91.66 \ g}{6.93 \ ml} = 13.21 \ g/ml$$

Therefore, the density of the metal is 13.21 g/ml.