I was looking to implicitly differentiate −22x^6+4x^(33)y+y^7=−17

I was looking to implicitly differentiate
$-22x^6+4x^{33}y+y^7=-17$
and found it to be
${\displaystyle \frac{dy}{dx}}={\displaystyle \frac{132x^5-132x^{32}y}{4x^{33}+7y^6}}$
Now, I am trying to find the equation of the tangent line to the curve at the coordinate (1,1). So I then plug both 1 in for x and y into the above equation and come up with
${\displaystyle \frac{0}{11}}$
Now I go to solve
$y-y1=m(x-x1)$
getting
$y-1=0(x-1)$
resulting in $y=1$ and the equation to be $y=x+1$ for my final answer. Am I going about this in the correct manner?