RGB to CMYK conversion problem

There is a situation where I have to transfer colors in Hex Format (from an app) to Adobe Illustrator. But I need to extract the exact CMYK value (that was assigned in the previous app). Long story short. Let's take an example:

There is a hex value: #ff7253

it's RGB = rgb(255,114,83)

and converted CMYK from RGB (using formulas) : cmyk(0,55,67,0) (conversion link: CMYK to RGB - RGB,CMYK,HEX color codes online converter free )

But If I insert the above RGB or Hex in adobe illustrator color picker:

input = rgb(255,114,83)

CMYK will be : cmyk(0,69,68,0)

and if I insert the CMYK value

input : cmyk(0,55,67,0)

output : rgb(246,141,94)

Kindly tell me how to resolve the issue. How can I get same value for CMYK conversion on Adobe Illustrator

( (RGB>CMYK with formulas) = (RGB>CMYK on illustrator) )?

Thanks in advance for your help.