To solve this expression, we need to follow the order of operations (PEMDAS).

6/5 + 1/6 ÷ (-3)

First, we need to simplify the division:

6/5 + 1/6 ÷ (-3) = 6/5 + 1/6 * (-1/3)

Next, we multiply the fractions:

6/5 + 1/6 * (-1/3) = 6/5 + (-1/18)

Now, we need to find a common denominator to add the fractions:

6/5 = 216/180
-1/18 = -10/180

Now we can add the fractions:

216/180 + (-10/180) = 206/180

Finally, we simplify the fraction:

206/180 = 103/90

Therefore, 6/5 + 1/6 ÷ (-3) = 103/90.