"Dual" ticks on colourbar

I have two functions f, g with different ranges but same domain. I visualize function f through a heatmap and function g through a contour map. To be able to plot them together I have to rescale g as seen in the code below. This way they have the same range.

using Plots

x = range(0, 10, 100)
y = range(0, 10, 100)

f = @. sin(x)' * sin(y)

g = (x, y) -> (x^2 - y ^2) * sin(x)*sin(y)

normalization = max(f...) / max(@. g(x', y)...)

desired_g_value = 1.

p = heatmap(x, y, f,
colorbar_title ="f")
contour!(p,
    x, 
    y, 
    (x ,y) ->  normalization * g(x, y),
    levels=normalization*desired_g_value:normalization*desired_g_value,
    clim=(-1, 1), # range of f
    c=:black
)   

This yields the following plot:

I would like to have at the left of the colorbar the ticks for the function g (before rescaling). Is it possible? If so, how?