To solve this equation, we first simplify the left side of the equation by combining like terms:

3x - 1/5 + 6x + 1/3
= 3x + 6x - 1/5 + 1/3
= 9x - 1/5 + 1/3

Next, let's find a common denominator to combine the fractions:

= (3 3x - 3 1/5 + 5 1/3) / (5 3)
= (9x - 3/5 + 5/3) / 15

Now we can combine the fractions:

= (9x - 9/15 + 25/15) / 15
= (9x + 16/15) / 15
= (9x + 16) / 15

The equation now becomes:

(9x + 16) / 15 = (3x - 1)^0

Since any number raised to the power of 0 is equal to 1, we have:

(9x + 16) / 15 = 1

Now, we can solve for x:

9x + 16 = 15
9x = -1
x = -1/9

Therefore, the solution to the equation is x = -1/9.