Since you have directed our attention to the question
How do i calculate Dice probability,
there are a few different parts to that question.
But the answer that you are trying to work with appears to be
https://math.stackexchange.com/a/478192,
which answers a very particular question:
Suppose I roll six fair six-sided dice. What is the probability that at least one of the dice will come up "$6$" when I roll them?
Assuming we can identify the dice
(the first die, the second die, and so forth),
there are $6^6$ possible outcomes we can distinguish, each outcome a
unique list of the numbers that appear on each die after rolling.
Since we said the dice were fair, each of these outcomes is equally likely.
If we consider rolling one or more $6$s to be a "favorable" outcome
and any other outcome is "not favorable",
there are $5^6$ "not favorable" (or "negative") outcomes
(the number of ways to have numbers $1,2,3,4,$ or $5$ on each of
$6$ dice).
That leaves $6^6 - 5^6$ "favorable" outcomes.
So if $A=6^6$, $B=5^6$, and $C$ is the probability of rolling at least
one $6$ on the six dice, then you have the correct formula:
$$
(A - B)/A = C.
$$
Plugging in the numeric values:
$$
(6^6 - 5^6)/6^6 = (46656 - 15625) / 46656 = 31031/ 46656
\approx 0.665102
$$
Some people would prefer to write this formula like this:
$$ C = \frac{A-B}{A}.$$
One can also use the fact
$$
\frac{A-B}{A} = 1 - \frac BA,
$$
that is, another version of this formula is
$$
C = 1 - \frac BA.
$$
Notice that
$$ \frac{6^6 - 5^6}{6^6} = 1 - \frac{5^6}{6^6}.$$
Again, $(6^6 - 5^6)/6^6$ is the probability you roll at least one $6$
when you roll six dice;
$5^6/6^6$ is the probability that you do not roll even one $6$
when you roll six dice.
So you have some formulas that are correct answers to some questions.
On the other hand, you have tried to use some incorrect formulas.
The difference $6^6 - 5^6$ is not equal to $1^6$,
and $(6^6 -1^6)/ 6^6$ is not equal to $5^6/6^6.$
